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Sup-Norm Error under Proportional Asymptotics: Phase Transitions under Linear Regression

NeurIPS 2026 · Learning theory and algorithms › Kernels and regression theory · approach: High-dimensional linear regression theory

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AI-extracted summary. Written by AI from the paper's abstract only. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.

Characterizes sharp asymptotics of the l-infinity estimation error for linear regression coefficients under proportional asymptotics, showing a signal-structure-dependent phase transition.

Problem

Sharp characterization of the l-infinity norm estimation error of regression coefficients in linear regression under proportional asymptotics, which is less studied than the l2 error.

Approach

Shows that the l-infinity error exhibits a distinct phase transition governed by the structure of the underlying signal, analyzed through a class of estimators (the abstract is truncated, so the specific estimator family is not stated).

Experimental setup

Metrics: l-infinity norm estimation error

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